STAT 242b/542b THEORY OF STATISTICS

Homework Assignments from text by Rice ``Mathematical Statistics and Data Analysis.''

HOMEWORK 1: Assigned Jan 14. Due Wednesday January 23. Probability review.

Chapter 1: problems 53,63
Chapter 2: problems 21,34,53
Chapter 3: problem 19,33,37,52
Chapter 4: problems 5,32,58.

HOMEWORK 2:  Due Wednesday January 30.  Some more probability for statistics.

Chapter 4: problem 97
Chapter 5: problems 3,14,17,26
Chapter 6: problems 4,6,7,9,11.

HOMEWORK 3:  Due Wednesday February 6.
Fitting distributions, computing maximum likelihood and method of moments estimators
and sufficient statistics.

Chapter 8: problems 1, 6,
problems 5 (parts a,b) ,10, 14 (parts a,b,d), 17 (parts a,b), 19, 54.

HOMEWORK 4:  Due Wednesday February 13.  Sampling distributions of estimators, asymptotics.

Chapter 8: problems 5 (part c), 8, 11, 14 (part c), 25, 44.

HOMEWORK 5:  Due Wednesday February 20.
Relative efficiency (comparing risks of estimators).
Cramer-Rao inequality. Minimum risk unbiased estimators

Chapter 8: problems 17 (part c), 40, 41, 45, 49, 52, 62.

HOMEWORK 6: Due Wednesday February 27.  Tests of statistical hypotheses.

Chapter 9:  problems 1, 2, 3, 7, 8, 10, 11.

HOMEWORK 7: Due Friday March 8.  Goodness of fit tests.

Chapter 9: problems 17, 25, 30, 33.

HOMEWORK 8: Due Wednesday April 3.  Comparing two samples.

Chapter 11: problems 3, 15, 16, 33, 34,
problem 38 (parts a,b,c,d,e, plus construct side-by-side boxplots).

HOMEWORK 9: Due Wednesday April 10.
Comparing several means and the analysis of variance.
You may restrict attention to parametric tests on these problems.

Chapter 12: problems 3, 14, 19, 24, 27.
Extra Credit: problem 26, derive and use a generalized likelihood ratio test for equality
of the three means based on an exponential distribution rather than a normal distribution.

HOMEWORK 10: Due Wednesday April 17.  Linear Models.

Chapter 14: problems 2, 4, 11, 16, 21, 33

HOMEWORK 11: Due Wednesday April 24. More on Regression and Prediction
Brief access to a computer is needed for problem 44.
I could not find the associated data set on the diskette provided with the text.
The other problems can be done by hand.

Chapter 14: problems 12, 19,  25, 38, 44

HOMEWORK 12: Due the last day of class
(Monday April 29 for main section, Tuesday April 30 for Pfizer section).
The problem (given below) involves a number of scatter plots, various transformations,
regression runs with various subsets, model selection, and residual plots.
Extensive access to a computer is required.  You may work closely with
a classmate on this one. Link to the data folder.

Chapter 14: problem 45.
[Parts a,b,c, plus compare models you construct using the Final Prediction Error (FPE) criterion
described in the supplementary class notes.  Note also: the FPE value computed from the
training data should predict well the RMSPE from the withheld data.  Is that true here?]